Question: If $a + b + c = 8$ and $x + y + z = 2$, what is $-9y - 9z + 2a + 2c - 9x + 2b$ ?
Solution: $= 2a + 2b + 2c - 9x - 9y - 9z$ $= (2) \cdot (a + b + c) + (-9) \cdot (x + y + z)$ $= (2) \cdot (8) + (-9) \cdot (2)$ $= 16 - 18$ $= -2$